Not with a crappy low level SMG. He needs a decent weapon, because he struggles VS armor. He will kill mooks with overload and headshots easily, but when the big boys come, he needs DPS. And GI is way better in that regard, because of 20% debuff from PM and raw cloak damage.
Well, the GI is possibly the most powerful character there is, but I still wouldn't prefer him to the GE for SMG challenges. I played a Gold game as a GE with CSMG at level II, where Arkhne more or less had to tell me to slow down. I admit I did run out of ammo a few times in later waves, but that was more to do with being used to the gun at level X. I adore the GPSMG (with incendiary) on the GE to the point that it's actually my preferred weapon for him. And 'when the big boys come' is about the only time that it needs its ramp-up - which works absolutely fine. I often begin tackling bosses by shooting straight into the soft cover in front of me for a second or so, so that I'm only exposed while doing maximum damage. There are of course better guns which can kill things faster, but there is no better character for the GPSMG (or even some of the other SMGs) than the GE.
If using the Locust for challenges (another genuine favourite of mine), I recommend using a scope and focusing on headshots - any Engineer or Turian should do the job nicely. I like the Tempest most on the Fury, and the BPP is great on the Vorcha Soldier too.
Conversely, I really hate the Hornet, and in more than 2.5k hours I've only scored 1760 points with the Shuriken, and will never add to that tally. 